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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Two teachers, Ms. Ames and Mr. Betancourt, each had N tagged by: BTGmoderatorLU ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Two teachers, Ms. Ames and Mr. Betancourt, each had N ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: Magoosh Two teachers, Ms. Ames and Mr. Betancourt, each had N cookies. Ms. Ames was able to give the same number of cookies to each one of her 24 students, with none left over. Mr. Betancourt also able to give the same number of cookies to each one of his 18 students, with none left over. What is the value of N? 1) N < 100 2) N > 50 The OA is A. ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1975 messages Followed by: 30 members Upvotes: 470 Top Reply BTGmoderatorLU wrote: Source: Magoosh Two teachers, Ms. Ames and Mr. Betancourt, each had N cookies. Ms. Ames was able to give the same number of cookies to each one of her 24 students, with none left over. Mr. Betancourt also able to give the same number of cookies to each one of his 18 students, with none left over. What is the value of N? 1) N < 100 2) N > 50 The OA is A. As per the information, we have N is a multiple of 24 and 18. Say, N/24 = p, where p is a positive integer; => N = 24p N/18 = p, where q is a positive integer; => N = 18q => 24p = 18q 4p = 3q => p = 3q/4 => q must be a multiple of 4 q: {4, 8, 12, 16, 20, ...} Thus, the corresponding values of N are: {72, 144, 288, 360, ...} If we get the unique value of p or q, we get the answer. Let's take each statement one by one. 1) N < 100 From the set for N: {72, 144, 288, 360, ...}, we have N = 72. Sufficient. 2) N > 50 From the set for N: {72, 144, 288, 360, ...}, we have {72, 144, 288, 360, ...}. No uniue value of N. Insufficient. The correct answer: A Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: Manhattan Review India | Himayatnagar GMAT Coaching | Dilsukhnagar GMAT Courses | Manhattan Review Hyderabad | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 BTGmoderatorLU wrote: Source: Magoosh Two teachers, Ms. Ames and Mr. Betancourt, each had N cookies. Ms. Ames was able to give the same number of cookies to each one of her 24 students, with none left over. Mr. Betancourt also able to give the same number of cookies to each one of his 18 students, with none left over. What is the value of N? 1) N < 100 2) N > 50 $$\left\{ \matrix{ \left( {{\rm{Ames}}} \right)\,\,N = 24 \cdot Q\,\,,\,\,Q \ge 1\,\,{\mathop{\rm int}} \hfill \cr \left( {{\rm{Betan}}} \right)\,\,N = 18 \cdot K\,\,,\,\,K \ge 1\,\,{\mathop{\rm int}} \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,N = LCM\left( {24,18} \right) \cdot J\,\,,\,\,J \ge 1\,\,{\mathop{\rm int}}$$ (N is a multiple of 18 and also a multiple of 24, hence N must be a multiple of the LCM of 18 and 24.) $$LCM\left( {{2^3} \cdot 3,2 \cdot {3^2}} \right) = {2^3} \cdot {3^2} = 72\,\,\,\,\,\,\,\, \Rightarrow \,\,\,N = 72 \cdot J\,\,,\,\,J \ge 1\,\,{\mathop{\rm int}}$$ $$? = N$$ $$\left( 1 \right)\,\,N < 100\,\,\,\,\, \Rightarrow \,\,\,\,J = 1\,\,\,\, \Rightarrow \,\,\,\,? = 72$$ $$\left( 2 \right)\,\,N > 50\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,J = 1\,\,\,\, \Rightarrow \,\,\,\,? = 72 \hfill \cr \,{\rm{Take}}\,\,J = 2\,\,\,\, \Rightarrow \,\,\,\,? = 144 \hfill \cr} \right.$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorLU wrote: Source: Magoosh Two teachers, Ms. Ames and Mr. Betancourt, each had N cookies. Ms. Ames was able to give the same number of cookies to each one of her 24 students, with none left over. Mr. Betancourt also able to give the same number of cookies to each one of his 18 students, with none left over. What is the value of N? 1) N < 100 2) N > 5. Since the N cookies can be divided evenly among 24 or 18 students, N must be divisible by both 24 and 18. One way to determine the LCM of two integers is to take multiples of the LARGER integer until we get a multiple of the SMALLER integer. Multiples of 24: 24, 48, 72... We can stop here: the value in blue is divisible by 18, since 72/18 = 4. Thus, the LCM of 24 and 18 = 72. Implication: Since the N cookies can be divided evenly among 24 or 18 students, N must be a positive MULTIPLE OF 72. Statement 1: N < 100 Thus, N=72. SUFFICIENT. Statement 2: N > 50 Here, N can be any positive multiple of 72. INSUFFICIENT. The correct answer is A. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! 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